Localised Arrowheads: The building blocks of elastic turbulence in rectilinear, sheared polymer flows
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910150968737792 |
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| author | Lewy, Theo A. Kerswell, Rich R. |
| author_facet | Lewy, Theo A. Kerswell, Rich R. |
| contents | Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organised around the interactions of localised versions of 2-dimensional `arrowhead' travelling waves (Page et al. Phys. Rev. Lett. 125, 154501, 2020). As a step to confirming this theoretically, we identify spanwise-localised arrowhead travelling waves by tracking a symmetry-breaking bifurcation of the known spanwise-invariant (2D) arrowhead to a spanwise-periodic state and then discovering a secondary modulational instability to a spanwise-localised travelling wave. Spanwise-symmetric and asymmetric localised arrowheads exist with the latter having a phase speed slightly inclined to the streamwise direction. Computations capture the flow randomly switching between spanwise local and global arrowhead states in a streamwise-restricted domain, suggesting they form the building blocks of the chaos. Splitting events are also seen, in which a single localised state spawns multiple arrowheads. However, both cross-shear and spanwise velocities are small suggesting that this elastic turbulence will not be a good mixer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localised Arrowheads: The building blocks of elastic turbulence in rectilinear, sheared polymer flows Lewy, Theo A. Kerswell, Rich R. Fluid Dynamics Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organised around the interactions of localised versions of 2-dimensional `arrowhead' travelling waves (Page et al. Phys. Rev. Lett. 125, 154501, 2020). As a step to confirming this theoretically, we identify spanwise-localised arrowhead travelling waves by tracking a symmetry-breaking bifurcation of the known spanwise-invariant (2D) arrowhead to a spanwise-periodic state and then discovering a secondary modulational instability to a spanwise-localised travelling wave. Spanwise-symmetric and asymmetric localised arrowheads exist with the latter having a phase speed slightly inclined to the streamwise direction. Computations capture the flow randomly switching between spanwise local and global arrowhead states in a streamwise-restricted domain, suggesting they form the building blocks of the chaos. Splitting events are also seen, in which a single localised state spawns multiple arrowheads. However, both cross-shear and spanwise velocities are small suggesting that this elastic turbulence will not be a good mixer. |
| title | Localised Arrowheads: The building blocks of elastic turbulence in rectilinear, sheared polymer flows |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2509.26168 |